Question

For Chapter 2 through Chapter 14, the Cumulative Review Exercises include topics from preceding chapters. For this chapter, we present a few calculator warm-up exercises, with expressions similar to those found throughout this book. Use your calculator to find the indicated values.

In Exercises 9–12, the given expressions are designed to yield results expressed in a form of scientific notation. For example, the calculator-displayed result of 1.23E5 can be expressed as 123,000, and the result of 1.23E-4 can be expressed as 0.000123. Perform the indicated operation and express the result as an ordinary number that is not in scientific notation.

\({6^{14}}\)

Short answer

The exponential value \({6^{14}}\)in ordinary notation is equal to 78,364,164,096.

Step-by-step solution

Given information

The value \({6^{14}}\)is to be calculated.

Ordinary notation and scientific notation

Scientific notation is generally used to quote numbers that are either too small or too large. The number of decimals that can be written at a time can be limited using this notation.

Ordinary notation requires writing the numbers as it is with all the decimal places. To limit the amount of space required, the numbers are often approximated when written in ordinary notation.

Calculation of the value

The value\({6^{14}}\)can be expressed as:

\(\begin{array}{c}{6^{14}} = 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6\\ = 78364164096\end{array}\)

Thus, the value is obtained to be equal to 78,364,164,096.